If I cut something into 3 equal pieces, there are 3 defined pieces. But, 1÷3= .333333~. Why is the math a nonstop repeating decimal when existence allows 3 pieces? Is the assumption that it’s physically impossible to cut something into 3 perfectly even pieces?
In: Mathematics
Want to break your head? 0.999… = 1.
1. 1/3 is 0.333 repeating: 1/3 = 0.333…
2. Multiply both sides by 3 to get rid of the fraction: 1/3 * 3 = 0.333… * 3
3. 3/3 = 0.999…
4. 1 = 0.999…
Want to get weirder? Try multiplying 0.999… by 10, which is just moving the decimal one spot to the right.
1. 10 * 0.999… = 9.999…
2. Now get rid of that annoying decimal by subtracting 0.999… from both sides: 10 * (0.999…) – 1 * (0.999…) = 9.999… – 0.999…
3. The left hand side of the equation is just 9 x (0.999…) because 10 times something minus that something is 9 times the aforementioned thing. And on the right hand side, we’ve canceled out the decimal.
4. 9 * (0.999…) = 9
5. If 9 times something is 9, that thing must be 1.
Lots more fun stuff in the chapter, Straight Logically Curved Globally from the book [How Not to Be Wrong: The Power of Mathematical Thinking](https://smile.amazon.com/How-Not-Be-Wrong-Mathematical/dp/0143127535), by Jordan Ellenberg.
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